1. Consider the regression model: M] = ßo = ß1 × UR where MJ is the past-month marijuana-use rate for 12-17 year-olds in a state in 2009-10, UR is the average state unemployment rate for 2009-10, and there are 51 observations (50 states plus DC). The results are the following, with the standard errors in parentheses below the coefficient estimate: %3D M) = 8.971 + 0.244 × UR (1.406) (0.148) a. Give the formal null and alternative hypotheses for whether the variable UR has a coefficient that is different from zero. b. Give the formal null and alternative hypotheses for whether the variable UR has a positive coefficient. c. Calculate the t-stat for the coefficient estimate on UR.

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1. Consider the regression model: M] = ßo = ß1 × UR where MJ is the past-month marijuana-use rate
for 12-17 year-olds in a state in 2009-10, UR is the average state unemployment rate for 2009-10, and
there are 51 observations (50 states plus DC). The results are the following, with the standard errors in
parentheses below the coefficient estimate:
M] :
= 8.971 + 0.244 × UR
(1.406) (0.148)
a. Give the formal null and alternative hypotheses for whether the variable UR has a coefficient that is
different from zero.
b. Give the formal null and alternative hypotheses for whether the variable UR has a positive coefficient.
c. Calculate the t-stat for the coefficient estimate on UR.
d. Determine the critical values for the two-sided test on that coefficient for tests at the 1%, 5%, and
10% levels. Is the coefficient estimate statistically significant at each of those levels?
e. Determine the critical value for the one-sided hypothesis test (at the 5% significance level) on that
estimate to test if it is positive. What is the conclusion of the hypothesis test?
f. Calculate the 95% confidence interval for the coefficient estimate on UR.
Transcribed Image Text:1. Consider the regression model: M] = ßo = ß1 × UR where MJ is the past-month marijuana-use rate for 12-17 year-olds in a state in 2009-10, UR is the average state unemployment rate for 2009-10, and there are 51 observations (50 states plus DC). The results are the following, with the standard errors in parentheses below the coefficient estimate: M] : = 8.971 + 0.244 × UR (1.406) (0.148) a. Give the formal null and alternative hypotheses for whether the variable UR has a coefficient that is different from zero. b. Give the formal null and alternative hypotheses for whether the variable UR has a positive coefficient. c. Calculate the t-stat for the coefficient estimate on UR. d. Determine the critical values for the two-sided test on that coefficient for tests at the 1%, 5%, and 10% levels. Is the coefficient estimate statistically significant at each of those levels? e. Determine the critical value for the one-sided hypothesis test (at the 5% significance level) on that estimate to test if it is positive. What is the conclusion of the hypothesis test? f. Calculate the 95% confidence interval for the coefficient estimate on UR.
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